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  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "from IPython.html.widgets import interact\n",
      "from scipy import  stats\n",
      "import seaborn as sns\n",
      "import pandas as pd"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Previously, we talk about maximum likelihood estimation and maximum a-posteriori estimation and in each case we started out with a probability density function of some kind and we further assumed that the samples were identically distributed and independent. The idea behind robust statistics is to construct estimators that can survive the weakening of either or both of these assumptions.\n",
      "\n",
      "The first idea to consider is the notion of *location*, which is  a generalization of the idea of \"central value\". Typically, we just use an estimate of the mean for this, but we will see shortly why that is a bad idea.  The general idea of Location satisfies the following requirements\n",
      "\n",
      "Let $ X $ be a random variable with distribution $ F $, and let $\\theta(X)$ be some descriptive\n",
      "measure of $F$. Then $\\theta(X)$ is said to be a measure of *location* if for any constants *a* and *b*, we have the following:\n",
      "\n",
      "$$ \\theta(X+b) = \\theta(X) +b $$\n",
      "\n",
      "$$ \\theta(-X) = -\\theta(X)$$\n",
      "\n",
      "$$ X \\ge 0 \\Rightarrow \\theta(X)  \\ge 0 $$\n",
      "\n",
      "$$ \\theta(a X) = a\\theta(X) $$\n",
      "\n",
      "The first condition is called *location equivariance* (or *shift-invariance*  in signal processing lingo). The fourth condition is called *scale equivariance*, which means that the units that $X$ is measured in should not effect the value of the  location estimator.  These Requirements capture the idea of what we intuitively mean by *centrality* of a distribution, or where most of the probability mass is located.\n",
      "\n",
      "For example, the mean estimator is $ \\hat{\\mu}=\\frac{1}{n}\\sum X_i $. The first requirement is obviously satisfied as $ \\hat{\\mu}=\\frac{1}{n}\\sum (X_i+b) = b +  \\frac{1}{n}\\sum X_i =b+\\hat{\\mu}$. Let us consider the second requirement:$ \\hat{\\mu}=\\frac{1}{n}\\sum -X_i = -\\hat{\\mu}$. Finally, the last requirement is satisfied with $ \\hat{\\mu}=\\frac{1}{n}\\sum a X_i =a \\hat{\\mu}$."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "What do we mean by robust estimators?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now that we have the generalized location of centrality embodied in the *location* parameter, what can we do with it?  The next idea is to nail down is the concept of * robust* estimators. Previously, we assumed that our samples were all identically distributed. The key idea is that the samples might be actually coming from a distribution that is contaminated by another nearby distribution, as in the following:\n",
      "\n",
      "$$ F(X) = \\epsilon G(X) + (1-\\epsilon)H(X) $$\n",
      "\n",
      "where $ \\epsilon $ is between zero and one. This means that our data samples $\\lbrace X_i \\rbrace$ actually derived from two separate distributions, $ G(X) $ and $ H(X) $. We just don't know how they are mixed together. What we really want  is an estimator  that captures the location of $ G(X) $ in the face of random intermittent contamination by $ H(X) $. It can get even worse than that because we don't know that there is only one contaminating $H(X)$ distribution out there. There may be a whole family of distributions that are contaminating $G(X)$ that we don't know of. This means that whatever estimators we construct have to be derived from families of distributions instead of a distribution, which is what we have been assuming for maximum-likelihood  estimators. This is what makes robust estimation so difficult --- the extended theory has to deal with spaces of function distributions instead of particular parameters of a particular probability distribution.\n",
      "\n",
      "* Influence function\n",
      "* Outlier Detection\n",
      "* Estimates of location\n",
      "    - definition of location\n",
      "* Trimmed means\n",
      "* Windsorized means\n",
      "* Hodges Lehmann statistics\n",
      "* Asymptotic efficiency\n",
      "* Fisher Consistent\n",
      "\n",
      "* Robust Regression \n",
      "    \n",
      "\n",
      "    - least median\n",
      "    - outliers"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n0=stats.norm(0,1)\n",
      "n1=stats.norm(1,2)\n",
      "xi = linspace(-5,5,100)\n",
      "\n",
      "fig,ax=subplots()\n",
      "ax.plot(xi,n0.pdf(xi))\n",
      "ax.plot(xi,n1.pdf(xi))\n",
      "\n",
      "def bias_coin(phead = .5):\n",
      "    while True:\n",
      "        yield int( np.random.rand() < phead ) \n",
      "\n",
      "pct_mixed  = 0.1\n",
      "bias_coin_gen = bias_coin(pct_mixed)        \n",
      "dual_set = [n0,n1]\n",
      "samples  = [ dual_set[bias_coin_gen.next()].rvs() for i in range(500) ]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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G93i74T1+f/ARzsw+lW8Xf5MI09JPsCKEJyRZC+ElwTxe3Tvex2OHn6V2oJ64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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1173a1b0>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "hist(samples,bins=20)\n",
      "title('average = %3.3f, median=%3.3f pct_mixed=%3.3f'%(mean(samples),np.median(samples),pct_mixed))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "<matplotlib.text.Text at 0x118ca270>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x11730930>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import sympy.stats\n",
      "from sympy.abc import x\n",
      "eps = sympy.symbols('epsilon')\n",
      "\n",
      "mixed_cdf = sympy.stats.cdf(sympy.stats.Normal('x',0,1),'x')(x)*(1-eps) + eps*sympy.stats.cdf(sympy.stats.Normal('x',1,2),'x')(x)\n",
      "mixed_pdf = sympy.diff(mixed_cdf,x)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plot_mixed_dist(epsilon=.1):\n",
      "    n1 = stats.norm(1,2)\n",
      "    xi = linspace(-5,5,100)\n",
      "    fig,ax = subplots()\n",
      "    ax.plot(xi,[sympy.lambdify(x,mixed_pdf.subs(eps,epsilon))(i) for i in xi],label='mixed',lw=2)\n",
      "    ax.plot(xi,n0.pdf(xi),label='g(x)',linestyle='--')\n",
      "    ax.plot(xi,n1.pdf(xi),label='h(x)',linestyle='--')\n",
      "    ax.legend(loc=0)\n",
      "    ax.set_title('epsilon = %2.2f'%(epsilon))\n",
      "    ax.vlines(0,0,.4,linestyle='-',color='g')\n",
      "    ax.vlines(epsilon,0,.4,linestyle='-',color='b')\n",
      "\n",
      "interact(plot_mixed_dist,epsilon=(0,1,.05))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "<function __main__.plot_mixed_dist>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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hsP+If8jW4gi/uWy0JcPjrfcdaaG2u4GGniaTIxIiMkiyFiIMHevop7VrgMQ4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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x12d214f0>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "M-estimators"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "M-estimators are generalized maximum likelihood estimators. Recall that for maximum likelihood, we want to maximize the likelihood function as in the following:\n",
      "\n",
      "$$ L_{\\mu}(x_i) = \\prod f_0(x_i-\\mu)$$\n",
      "\n",
      "and then to find the estimator $\\hat{\\mu}$ so that\n",
      "\n",
      "$$ \\hat{\\mu} = \\arg \\max_{\\mu} L_{\\mu}(x_i) $$\n",
      "\n",
      "So far, everything is the same as our usual maximum-likelihood  derivation except for the fact that we don't know $f_0$, the distribution of the $\\lbrace X_i\\rbrace$. Making the convenient definition of\n",
      "\n",
      "$$ \\rho = -\\log f_0 $$\n",
      "\n",
      "we obtain the more convenient form of the likelihood product and the optimal $\\hat{\\mu}$ as\n",
      "\n",
      "$$ \\hat{\\mu} = \\arg \\min_{\\mu} \\sum \\rho(x_i-\\mu)$$\n",
      "\n",
      "If $\\rho$ is differentiable, then differentiating  this with respect to $\\mu$ gives\n",
      "\n",
      "$$ \\sum \\psi(x_i-\\hat{\\mu}) = 0 $$\n",
      "\n",
      "with $\\psi = \\rho'$ and for technical reasons we will assume that $\\psi$ is increasing. The key idea here is we want to consider general $\\rho$ functions that my not be MLE for *any* distribution.\n"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "The distribution of  M-estimates "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For a given distribution $F$, we define $\\mu_0=\\mu(F)$ as the solution to the following \n",
      "\n",
      "$$ \\mathbb{E}_F(\\psi(x-\\mu_0))= 0 $$\n",
      "\n",
      "It is technical to show, but it turns out that $\\hat{\\mu} \\sim \\mathcal{N}(\\mu_0,\\frac{v}{n})$ with\n",
      "\n",
      "$$ v = \\frac{\\mathbb{E}_F(\\psi(x-\\mu_0)^2)}{(\\mathbb{E}_F(\\psi^\\prime(x-\\mu_0)))^2} $$\n",
      "\n",
      "Thus, we can say that $\\hat{\\mu}$ is asymptotically normal with asymptotic value $\\mu_0$ and asymptotic variance $v$. This leads to the efficiency ratio which is defined as  the following:\n",
      "\n",
      "$$ \\texttt{Eff}(\\hat{\\mu})= \\frac{v_0}{v} $$\n",
      "\n",
      "where $v_0$ is the asymptotic variance of the MLE and measures how near $\\hat{\\mu}$ is to the optimum. for example, if for two estimates with asymptotic variances $v_1$ and $v_2$, we have $v_1=3v_2$, then first estimate requires three times as many observations to obtain the same variance as the second.\n",
      "\n",
      "For example, for the sample mean (i.e. $\\hat{\\mu}=\\frac{1}{n} \\sum X_i$) with $F=\\mathcal{N}$, we have $\\rho=x^2/2$ and $\\psi=x$ and also $\\psi'=1$. Thus, we have $v=\\mathbb{V}(x)$. Alternatively, using the sample median as the estimator for the location, we have $v=\\frac{1}{4 f(\\mu_0)^2}$. Thus, if we have $F=\\mathcal{N}(0,1)$, for the sample median, we obtain $v=\\frac{2\\pi}{4} \\approx 1.571$. This means that the sample median takes approximately 1.6 times as many samples to obtain the same variance for the location as the sample mean."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "One way to think about M-estimates is a weighted means. Most of the time, we have $\\psi(0)=0$ and $\\psi'(0)$ exists so that $\\psi$ is approximately linear at the origin. Using the following definition:\n",
      "\n",
      "\n",
      "$$ W(x)  =  \\begin{cases}\n",
      "                \\psi(x)/x & \\text{if} \\: x \\neq 0 \\\\\n",
      "                \\psi'(x)  & \\text{if} \\: x =0 \n",
      "            \\end{cases}\n",
      "$$\n",
      "\n",
      "We can write our earlier equation as follows:\n",
      "\n",
      "$$ \\sum W(x_i-\\hat{\\mu})(x_i-\\hat{\\mu}) = 0 $$\n",
      "\n",
      "Solving this for $\\hat{\\mu} $ yields the following,\n",
      "\n",
      "$$ \\hat{\\mu} = \\frac{\\sum w_{i} x_i}{\\sum w_{i}} $$\n",
      "\n",
      "where $w_{i}=W(x_i-\\hat{\\mu})$. The question that remains is how to pick the $\\psi$ functions."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Huber functions"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The family of Huber function is defined by the following:\n",
      "\n",
      "$$ \\rho_k(x ) = \\begin{cases}\n",
      "                x^2  & \\text{if} \\: |x|\\le k \\\\\n",
      "                2 k |x|-k^2 & \\text{if} \\: |x| \\gt k\n",
      "                \\end{cases}\n",
      "$$\n",
      "\n",
      "with corresponding derivatives $2\\psi_k(x)$ with\n",
      "\n",
      "$$ \\psi_k(x ) = \\begin{cases}\n",
      "                x  & \\text{if} \\: |x|\\le k \\\\\n",
      "                \\text{sgn}(x)k & \\text{if} \\: |x| \\gt k\n",
      "                \\end{cases}\n",
      "$$\n",
      "where the limiting cases $k \\rightarrow \\infty$ and $k \\rightarrow 0$ correspond to the mean and median, respectively. To see this, take $\\psi_{\\infty} = x$ and therefore $W(x) = 1$ and thus the defining equation results in\n",
      "\n",
      "$$ \\sum_{i=1}^{n} (x_i-\\hat{\\mu}) = 0 $$\n",
      "\n",
      "and then solving this leads to $\\hat{\\mu} = \\frac{1}{n}\\sum x_i$. Note that choosing $k=0$ leads to  the sample median, but that is not so straightforward to solve for."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig,ax=subplots()\n",
      "colors=['b','r']\n",
      "for k in [1,2]:\n",
      "    ax.plot(xi,np.ma.masked_array(xi,abs(xi)>k),color=colors[k-1])\n",
      "    ax.plot(xi,np.ma.masked_array(np.sign(xi)*k,abs(xi)<k),color=colors[k-1],label='k=%d'%k)\n",
      "ax.axis(ymax=2.3,ymin=-2.3)\n",
      "ax.set_ylabel(r'$\\psi(x)$',fontsize=28)\n",
      "ax.set_xlabel(r'$x$',fontsize=24)\n",
      "ax.legend(loc='best')\n",
      "ax.set_title('Huber functions')\n",
      "ax.grid()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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IRwMLYozTQwgHJ50nz1UCw4CzY4zPhBCuBX4IjF7dwSUhxnj46j4W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\nUlaWBEmSlJUlQZIkZfX/AOEfq8litHg3AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x12df27b0>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The $W$ function corresponding to Huber's $\\psi$ is the following:\n",
      "\n",
      "$$ W_k(x) = \\min\\Big{\\lbrace} 1, \\frac{k}{|x|} \\Big{\\rbrace} $$\n",
      "\n",
      "which is plotted in the following cell for a few values of $k$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig,ax=subplots()\n",
      "ax.plot(xi,np.vstack([np.ones(xi.shape),2/abs(xi)]).min(axis=0),label='k=2')\n",
      "ax.plot(xi,np.vstack([np.ones(xi.shape),1/abs(xi)]).min(axis=0),label='k=1')\n",
      "ax.axis(ymax=1.1)\n",
      "ax.legend(loc=0)\n",
      "ax.set_title(\"Huber's weight function\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "<matplotlib.text.Text at 0x12dd82d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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uO5v3teC12JahYnZIURZhNeH28MGBNlITXSwuTjc6zklrHGwmxZVMkivR6ChR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\nqlhZsIo91Qdoc7VZHa3P0pmyh3O2OllftoVdVfs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       "text": [
        "<matplotlib.figure.Figure at 0x12df0050>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Another alternative intuitive way  to interpret  the M-estimate is to rewrite the following:\n",
      "\n",
      "$$ \\hat{\\mu} = \\hat{\\mu} +\\frac{1}{n}\\sum_i \\psi(x_i-\\hat{\\mu}) = \\frac{1}{n} \\sum_i \\zeta(x_i,\\hat{\\mu})$$\n",
      "\n",
      "which for the Huber family of functions takes on the form :\n",
      "\n",
      "$$ \\zeta(x,\\mu) = \\begin{cases}\n",
      "                    \\mu - k & \\text{if} \\: x \\lt \\mu-k \\\\\n",
      "                    x & \\text{if} \\: \\mu-k \\le x \\le \\mu+k \\\\\n",
      "                    \\mu+k & \\text{if} \\: x \\gt \\mu \\\\\n",
      "                  \\end{cases}\n",
      "$$\n",
      "\n",
      "Thus, the interpretation here is that $\\hat{\\mu}$ is the average of the truncated pseudo-observations $\\zeta_i$ where the observations beyond a certain point are clipped at the $k$-offset of the $\\hat{\\mu}$. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "kvals= [.001,0.3,0.5,.7,1.00001,1.4,1.7,2,3,4,5]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pythonica\n",
      "mma=pythonica.Pythonica()\n",
      "mma.plot_dir='.'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def closure_variance(mn=(0,1),std=(1,1)):\n",
      "    # close over specific F-distribution and integral terms\n",
      "    mma.eval('Clear[\"`*\"]') # clear workspace\n",
      "    mma.eval('lpdf=D[CDF[NormalDistribution[%g,%g], x](1-Epsilon)+Epsilon*CDF[NormalDistribution[%g,%g],x],x]'%(mn[0],std[0],mn[1],std[1]))\n",
      "    denom=mma.eval('Integrate[lpdf,{x,-k,k},Assumptions -> k > 0]^2')\n",
      "    numer=mma.eval('Integrate[lpdf*Piecewise[{{x, Abs[x] < k},{k*Sign[x],Abs[x] >= k}}]^2, {x, -Infinity, Infinity}, Assumptions -> k > 0]')\n",
      "    def asymp_variance(kval,eps=0.01):\n",
      "        mma.push('k',kval)\n",
      "        mma.push('Epsilon',eps)\n",
      "        mma.eval('numer ='+numer) # used closure string\n",
      "        mma.eval('denom ='+denom)\n",
      "        mma.eval('Clear[k,Epsilon]')\n",
      "        return float(mma.eval('N[numer/denom]'))\n",
      "    return asymp_variance"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "asympt_var_case1 = closure_variance((0,1),(1,2)) # case 1 with N(0,1) + N(1,2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig,ax=subplots()\n",
      "ax.plot(kvals,[asympt_var_case1(k,0) for k in kvals],'-o',label='eps=0')\n",
      "ax.plot(kvals,[asympt_var_case1(k,.05) for k in kvals],'-o',label='eps=.05')\n",
      "ax.plot(kvals,[asympt_var_case1(k,.1) for k in kvals],'-o',label='eps=0.1')\n",
      "ax.set_xlabel(\"k\")\n",
      "ax.set_ylabel(\"relative asymptotic efficiency \")\n",
      "ax.legend(loc=0)\n",
      "ax.set_title(r\"$\\mathcal{N}(0,1) , \\mathcal{N}(1,2)$ mixed\",fontsize=18)\n",
      "ax.grid()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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PzQ5h5EIIIUT4GNnPfLRS6nOl1A7f75OVUveFOa4OWcxmpoxO40hNI3r3Ib/l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\nbcPwEwgxdBLmI1QgGOKhFz9na42Lr80v5/LTp6Z1DWNv837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eWgm35jWksDhZSdO0cuBc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\nQogMJ2EuhBBCZDgJcyGEECLD/X94fwa7uASxPwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1173a4b0>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "asympt_var_case2 = closure_variance((0,0),(1,10)) # case 1 with N(0,1) + N(0,10)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig2,ax=subplots()\n",
      "ax.plot(kvals,[asympt_var_case2(k,0) for k in kvals],'-o',label='eps=0')\n",
      "ax.plot(kvals,[asympt_var_case2(k,.05) for k in kvals],'-o',label='eps=.05')\n",
      "ax.plot(kvals,[asympt_var_case2(k,.1) for k in kvals],'-o',label='eps=0.1')\n",
      "ax.set_xlabel(\"k\")\n",
      "ax.set_ylabel(\"relative asymptotic efficiency \")\n",
      "ax.legend(loc=0)\n",
      "ax.set_title(r\"$\\mathcal{N}(0,1) , \\mathcal{N}(0,10)$ mixed\",fontsize=18)\n",
      "ax.grid()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ZtI1WZACcEEJ0HIbLRc6bq8h/7x2s4eGkzLqZ0IGDzA6rQ2nVADhgAjAeOBb3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\nTfsE8L+VUtfOdU4J841jIbfKTYlE4/jGUwN+5odvPMRCf92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       "text": [
        "<matplotlib.figure.Figure at 0x117529d0>"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig.get_axes()[0].axis(ymax=3.5)\n",
      "fig"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "png": 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BXwALgf8HTAFe6k4BRUREpPu87Jr2R+B44J/AydbaOe6pR40xC7JZOBEREemc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\nLklS4f4FLCg0is2U0AoAAAAASUVORK5CYII=\n",
       "prompt_number": 22,
       "text": [
        "<matplotlib.figure.Figure at 0x1173a4b0>"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Computable Example"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nsamples = 200\n",
      "xs = np.array([dual_set[bias_coin_gen.next()].rvs() for i in range(200)*nsamples ]).reshape(nsamples,-1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig,ax=subplots()\n",
      "ax.hist(np.mean(xs,0),20,alpha=0.8,label = 'mean')\n",
      "ax.hist(np.median(xs,0),20,alpha=0.3,label ='median')\n",
      "ax.legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 24,
       "text": [
        "<matplotlib.legend.Legend at 0x12d21970>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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K+Zy09vTdawpGtii7mTfNa+EYMwAADiGYAQBwCMEMAIBDCGYAABxCMAMA4BCC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\nDPsindYAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x12d21710>"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "References"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "* Maronna, R. A., R. D. Martin, and V. J. Yohai. \"Robust Statistics: Theory and Methods\". 2006."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig,ax=subplots()\n",
      "sns.violinplot(np.vstack([np.median(xs,axis=0),np.mean(xs,axis=0)]).T,ax=ax,names=['median','mean']);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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rqqrk1df+zI7tW7Cl5ePuNExmdKegaKC26dp1oJZhw0cx7bob5b7rBNqxYzsv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\npBH2/yaxZd+Y/TK9AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1338cd90>"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mma.push('data',xs[:,0].tolist())\n",
      "mma.eval('psi[k_] := Function[x, Piecewise[{{x, Abs[x] < k}, {k*Sign[x], Abs[x] > k}}]]')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def psi_est(k,x):\n",
      "    if x.ndim ==2 : # loop over columns\n",
      "        out = []\n",
      "        for i in range(x.shape[1]):\n",
      "            data = x[:,i]\n",
      "            out.append( psi_est(k,data) ) # recurse\n",
      "        return np.array(out)\n",
      "    else:        \n",
      "        mma.push('data',x.tolist())\n",
      "        return float(mma.eval('\\[Mu] /. FindRoot[Plus @@ (psi[%d] /@ (data - \\[Mu])) == 0, {\\[Mu], 0}]'%(k)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "hist(psi_est(1,xs),alpha=.7,label='k=1')\n",
      "hist(psi_est(2,xs),alpha=.7,label='k=2')\n",
      "hist(psi_est(3,xs),alpha=.7,label='k=3')\n",
      "legend(loc=0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "<matplotlib.legend.Legend at 0x1313f750>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ntBLMAOC4qFJVOTOhTCYnSSp70+rL5FTOdGBdXk1PzcXy5lcHYFStKV/bqVw+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\n4BCCGQAAhxDMAAA4hGAGAMAh/x+iiYSmqd9mlwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x13489830>"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "huber_est={k:psi_est(k,xs) for k in [1,1.5,2,3]}\n",
      "huber_est[0] = np.median(xs,axis=0)\n",
      "huber_est[4] = np.mean(xs,axis=0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig,ax=subplots()\n",
      "sns.violinplot(pd.DataFrame(huber_est),ax=ax)\n",
      "ax.set_xticklabels(['median','1','1.5','2','3','mean']);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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g8NGDUySdtfjm6yMoksQc29gBivNtdrp6e2ZkkZiTJ4+hqfYxA8ni5HhmU1tb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\nHEwCtRBCCOFg/z/q2lrcRJzvNwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x13377810>"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sympy import mpmath, symbols, diff, Piecewise, sign, lambdify\n",
      "from sympy.stats import density, cdf, Normal\n",
      "from sympy.abc import k,x"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "eps = symbols('epsilon')\n",
      "lpdf=diff(cdf(Normal('x',0,1))(x)*(1-eps)+ eps*cdf(Normal('x',0,10))(x),x)\n",
      "p = Piecewise((x,abs(x)<k),(k*sign(x),True))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 32
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def asymptotic_variance(kval,epsval):\n",
      "    denom=mpmath.quad(lambdify(x,lpdf.subs(eps,epsval)),[-kval,kval])**2\n",
      "    numer=mpmath.quad(lambdify(x,(p.subs(k,kval))**2*lpdf.subs(eps,epsval)),[-kval*20,kval*20])\n",
      "    return float(numer/denom)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 33
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "asymptotic_variance(1,.05)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 34,
       "text": [
        "1.292336985078515"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "asympt_var_case2(1.0001,.05)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 35,
       "text": [
        "1.2625286610649238"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def closure_on_asymptotic_variance(mn=(0,0),std=(1,10)):\n",
      "    from sympy.abc import k,x\n",
      "    eps = symbols('epsilon')\n",
      "    lpdf=diff(cdf(Normal('x',mn[0],std[0]))(x)*(1-eps)+ eps*cdf(Normal('x',mn[1],std[1]))(x),x)\n",
      "    def asymptotic_variance(kval,epsval):\n",
      "        p = Piecewise((x,abs(x)<kval),(kval*sign(x),True))\n",
      "        denom=mpmath.quad(lambdify(x,lpdf.subs(eps,epsval)),[-kval,kval])**2\n",
      "        numer=mpmath.quad(lambdify(x,(p.subs(k,kval))**2*lpdf.subs(eps,epsval)),[-np.inf,np.inf])\n",
      "        return float(numer/denom)\n",
      "    return asymptotic_variance"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 72
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "case2=closure_on_asymptotic_variance()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 73
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print case2(1.0001,.05)\n",
      "print asympt_var_case2(1.0001,.05)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1.26296063799\n",
        "1.26252866106\n"
       ]
      }
     ],
     "prompt_number": 74
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig2,ax=subplots()\n",
      "ax.plot(kvals,[case2(k,0) for k in kvals],'-o',label='eps=0')\n",
      "ax.plot(kvals,[case2(k,.05) for k in kvals],'-o',label='eps=.05')\n",
      "ax.plot(kvals,[case2(k,.1) for k in kvals],'-o',label='eps=0.1')\n",
      "ax.plot(kvals,[asympt_var_case2(k,0) for k in kvals],'--o',label='mma eps=0')\n",
      "ax.plot(kvals,[asympt_var_case2(k,.05) for k in kvals],'--o',label='mma eps=.05')\n",
      "ax.plot(kvals,[asympt_var_case2(k,.1) for k in kvals],'--o',label='mma eps=0.1')\n",
      "ax.set_xlabel(\"k\")\n",
      "ax.set_ylabel(\"relative asymptotic efficiency \")\n",
      "ax.legend(loc=0)\n",
      "ax.set_title(r\"$\\mathcal{N}(0,1) , \\mathcal{N}(0,10)$ mixed\",fontsize=18)\n",
      "ax.grid()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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wB7BHKbUMeFVrvaWlA2xupp43kLr7ZayVRYAjkSf0v7dVrt0el0CtavToscyd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\nMSbwUWCNUurTlmU1AfVKqZ15iXKWFlsyh2wFuZ88fojOI72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       "text": [
        "<matplotlib.figure.Figure at 0x22e7d3d0>"
       ]
      }
     ],
     "prompt_number": 76
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}